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Yes, you're supposed to refer to "an hotel"
But very few people do.
So it depends whether you count correctness as being "that used by the majority" or "that used by pedants of the English language".
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It depends on how you pronounce hotel. If you sound the h then you should say a hotel. If you don't sound the h then it's an (h)otel.
This only applies to spoken English.
I was taught that an is used before a vowel and if vowel is not the next letter then a
To be correct, the h is silent, as in hour, so just as we refer to an hour, we should say an hotel.
Both in written and spoken English